A166364 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593735, 292968600, 1464842640, 7324211400, 36621048000, 183105195000, 915525750000, 4577627625000, 22888132500000, 114440634375000, 572203031250000

Offset

0,2

Comments

The initial terms coincide with those of A003948, although the two sequences are eventually different.

Computed with Magma using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (4,4,4,4,4,4,4,4,4,4,-10).

Formula

G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 10, -4, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 13 2016 *)

Prog

(SageMath)
def A166364_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12) ).list()
A166364_list(30) # G. C. Greubel, Mar 13 2020
(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)*(1+x)/(1-4*x-4*x^2-4*x^3-4*x^4-4*x^5-4*x^6-4*x^7-4*x^8-4*x^9-4*x^10+10*x^11)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026
(PARI) a(n)=if(n, ([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; -10, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]^(n-1)*[6; 30; 150; 750; 3750; 18750; 93750; 468750; 2343750; 11718750; 58593735])[1, 1], 1) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A003948, A154638.

Sequence in context: A164741 A165213 A165777 * A166500 A166877 A167107

Adjacent sequences: A166361 A166362 A166363 * A166365 A166366 A166367

Keyword

nonn,easy

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved